3 -1 20 - Let u1 = Uz = and y = 3 Uz = 3 -2 -4 Let W = span{u1, u2, U3} (i) Find the orthogonal projection of y onto the subspace W. (ii) Find dist(y, W).

Q: Which one of the following is a subspace of the vector space M2 (R) of 2 x 2 matrices? ss (X) the…

A: .

Q: 6. (a) Let u, v, w be three linearly independent vectors in Euclidean Space R^7. Determine a value…

A: we have to find the value of for the linearly dependent and linearly independent

Q: (a) Consider the real linear map T : R' - R', expressed as follows: (1 2 -1 49 -1 X1 X1 + 2x2 - x3…

A:

Q: 19. What is the value of (pk) when p is prime and k is a positive integer?

A: We know that the value of the Euler ϕ-function at the positive integer n is defined to be the number…

Q: If V is vector space, with u = (u, , U2) and v = (v, , v2) with u +v = (u,+v, , u2+v2) and ku =…

A: u=(u1,u2) , ku=(3u1,0) k=2, u=(-1,2)

Q: Determine whether the given series converges or diverges. If it converges, find its sun 8 Ž(¹+4)* a.…

A: Given series∑n=1∞(1+8n)n

Q: a. Write the solution set to the following equation in parametric vector form (consider ₁ to be the…

A:

Q: a) Let t: R">R be the Composite 3. linear transformation which means the vectors in R? are first…

A: Answer:

Q: Q-2: a) combination of the vectors X = (1,2,3,0) and Y = (2,1,6,0). b) a linearly independent set of…

A:

Q: 3. Let W C R be an inner product subspace with standard dot product. { 12 then If W I1- 2r2 + 4 = I3…

A:

Q: Find ProjS(u) where S is the space spanned by v1= (1/3)(2,1,2) and v2= (1/3)(-2,2,1). Find the…

A:

Q: c) Find dimension of subspace of all vectors in R° whose first and third entries are equal.

A: We have to find the dimensions

Q: function V(x,y,z) = x² + xy + yz and a vector A = x² + xy + yzź are given. a) Find VV(x, y, z). b)…

A: Given function v(x,y,z) is

Q: Use the function to find the image of v and the preimage of w. T(Vg, V2) = (V, + V2 V1 – V2), v =…

A:

Q: Let B' = {u1,u2} and ß = {v1,v2} be ordered bases for a 2-dimensional vector space V. Given that [u1…

A: Given u1+u2β=5,4t, and the change of coordinate matrix Q from β' to β is Q=1c3d. Express v1 as a…

Q: l₁ : (x, y, z) = (23, 98, -36) +r(8, 32, -12) where r ER and l₂ : (x, y, z) = (–9, −30, 12) + t2, 8,…

A: l1 = (23, 98, -36) + r (8, 32, -12) l2 = (-9, -30, 12) + t (2, 8, -3) The information we get from…

Q: Use the function to find the image of v and the preimage of w. T(V₁ V₂ V3) = (4V₂ - V₁₁ 4V₁ +5V₂), v…

A:

Q: 6. Project the vector b = (1, 4, 2) onto the plane S that contains the vectors a₁ = (1, 2, 1) and a2…

A:

Q: (b) Find two orthonormal vectors u₁, u₂ that span the same subspace of R³ as V₁ = [3,4,0]¹, V₂ =…

A: Here given vectors v1=340, v2=213

Q: 2. Linear maps Consider the following three vectors in R³: --0) --(9) +-0. V1 V3 = (a) Show that =…

A: Q.2 (a) asked and answered.

Q: 7) Determine whether the sets of vectors are linearly independent. а) {(-1, 2, 4)), (5, -10, -20);…

A: According to Bartleby guidelines I am supposed to do only first two questions . Kindly post next one…

Q: one example of a 4-dimensional vector space that is not R 4

A: